Given: G is the midpoint of EF

Question

proof<EHG is congruent <FHG

Answer 1

G is the midpoint of EFEF (Given).

This means: EG=FG

HG  is shared by △EHG  and △FHG  (Common side).

EH and FH  are the sides forming the angles ∠EHG and ∠FHG (Segments in the triangles).

By the Reflexive Property, HG‾=HG‾



In △EHGand △FHG:

1. EG=FG (Midpoint property),
2. HG‾=HG (Common side),
3. EH and FH meet at H (forming the two angles).

By the Base Angles Theorem (or congruence of triangles if needed), the angles opposite equal sides in an isosceles triangle are congruent:

∠EHG≅∠FHG..